One of the first known examples of step by step composing methods is credited to d’Arezzo (ca. 991- ca. 1028) who proposes, in chapter XVII of Micrologus (1025-26) (D’Arezzo 1978), an algorithm capable of outputting from any input common text a new array of notes as a melodic line.
The core idea behind Guido d'Arezzo’s algorithm can be reconstructed as the sequence of the following steps:
Step 1- create a two-dimensional table, each dimension with sixteen empty slots.
Step 2- fill the empty slots in the top dimension with the rising steps of the gamut
(G A B C D E F G a b c d e f g a), according to the standard vocal range.
Step 3- fill the empty slots in the bottom dimension with a cyclic sequence of all
vowels (a, e, i, o, u, a, e, i, o, u, a, e, i, o, u, a).
Step 4- given any input text, eliminate all consonants and retain all vowels in their
original order of appearance.
Step 5- take the first vowel, find it in the bottom dimension and replace it by the
corresponding pitch in the top-dimension.
Step 6- repeat Step 5 for each of the remaining vowels.
Step 7- if no more vowels, proceed to Step 8.
Step 8- Your melody is ready! You have the right to use or reject the output,
partially or in its entirety. For every pitch in the melody that you reject, you may
go back to Step 5 and look for a different slot that, while storing the same vowel,
corresponds to a pitch different than the one first obtained.
Guido d'Arezzo’s table look-up method can be divided into two different stages. The first stage is the transformation process of a vowel to one of the table’s possible corresponding pitches and, the second stage, based on stylistic preferences, is the selection of the best choice (Loy 1989).
Musical acrostics, a related strategy to Guido’s algorithm, derives the order of pitches in a theme from one or more words that, traditionally, hold a special interest to the composer. The Bb-A-C-H motive that J. S. Bach introduced in the last and unfinished fugue of the Art of the Fugue is a musical analogy of his own name, where the first and last letters of the name, B and H have been converted respectively to the pitches B flat and B natural. Numerous composers such as Beethoven in his String Quartet Op. 59 No. 2, Robert Schumann (1810-1856) in his Sechs Fugen über den Namen: Bach, Franz Liszt (1811- 1886) in his Fantasy and Fugue on B.A.C.H., Anton Webern (1883-1945) in his String Quartet Op. 28 and Pierre Boulez (1925- ) in his Second Piano Sonata have included the same four tones of the B-A-C-H motive, as a symbolic gesture of admiration to J. S. Bach.
Musical acrostics have also been used with programmatic intentions, as in, for example, Robert Schumann’s Abegg Variations, variations on the name of a lady friend spelled as A-Bb-E-G-G, and in the motto theme ‘ArnolD SCHönBErG’, ‘Anton wEBErn’ and ‘AlBAn BErG’ with which Alban Berg (1885-1935), in the opening of the Kammerkonzert, represents the three members of the Second Viennese School.
The core idea behind Guido d'Arezzo’s algorithm can be reconstructed as the sequence of the following steps:
Step 1- create a two-dimensional table, each dimension with sixteen empty slots.
Step 2- fill the empty slots in the top dimension with the rising steps of the gamut
(G A B C D E F G a b c d e f g a), according to the standard vocal range.
Step 3- fill the empty slots in the bottom dimension with a cyclic sequence of all
vowels (a, e, i, o, u, a, e, i, o, u, a, e, i, o, u, a).
Step 4- given any input text, eliminate all consonants and retain all vowels in their
original order of appearance.
Step 5- take the first vowel, find it in the bottom dimension and replace it by the
corresponding pitch in the top-dimension.
Step 6- repeat Step 5 for each of the remaining vowels.
Step 7- if no more vowels, proceed to Step 8.
Step 8- Your melody is ready! You have the right to use or reject the output,
partially or in its entirety. For every pitch in the melody that you reject, you may
go back to Step 5 and look for a different slot that, while storing the same vowel,
corresponds to a pitch different than the one first obtained.
Guido d'Arezzo’s table look-up method can be divided into two different stages. The first stage is the transformation process of a vowel to one of the table’s possible corresponding pitches and, the second stage, based on stylistic preferences, is the selection of the best choice (Loy 1989).
Musical acrostics, a related strategy to Guido’s algorithm, derives the order of pitches in a theme from one or more words that, traditionally, hold a special interest to the composer. The Bb-A-C-H motive that J. S. Bach introduced in the last and unfinished fugue of the Art of the Fugue is a musical analogy of his own name, where the first and last letters of the name, B and H have been converted respectively to the pitches B flat and B natural. Numerous composers such as Beethoven in his String Quartet Op. 59 No. 2, Robert Schumann (1810-1856) in his Sechs Fugen über den Namen: Bach, Franz Liszt (1811- 1886) in his Fantasy and Fugue on B.A.C.H., Anton Webern (1883-1945) in his String Quartet Op. 28 and Pierre Boulez (1925- ) in his Second Piano Sonata have included the same four tones of the B-A-C-H motive, as a symbolic gesture of admiration to J. S. Bach.
Musical acrostics have also been used with programmatic intentions, as in, for example, Robert Schumann’s Abegg Variations, variations on the name of a lady friend spelled as A-Bb-E-G-G, and in the motto theme ‘ArnolD SCHönBErG’, ‘Anton wEBErn’ and ‘AlBAn BErG’ with which Alban Berg (1885-1935), in the opening of the Kammerkonzert, represents the three members of the Second Viennese School.
